Yes, work = force * distance. There's also a relationship that says that work = difference in kinetic energy. If you can find the amount of potential energy that's been made into kinetic energy during the fall, you can find the amount of kinetic energy lost when the object pushes the pole down, which is then equal to the work done.

The force in W = F*d is the one you want to find. And the unit of work is not, as you say in your previous post, Newton. It's Joules :)